Mixed-Hybrid Transport Discretization Using Even and Odd P_N Expansions

References

• E. E. LEWIS and W. F. MILLER, Jr., Computational Methods of Neutron Transport, John Wiley & Sons, New York (1984).
   Google Scholar
• V. S. VLADIMIROV, “Mathematical Problems in the One-Velocity Theory of Particle Transport,” Technical Report, Atomic Energy of Canada Ltd. (1963); Translated from Trans. V. A. Steklov Mathematical Institute, 61 (1961).
   Google Scholar
• I. BABŬSKA, J. T. ODEN, and J. K. LEE, “Mixed-Hybrid Finite Element Approximations of Second-Order Elliptic Boundary-Value Problems,” Comput. Methods Appl. Mech. Eng., 11, 175 (1977).
   Web of Science ®Google Scholar
• S. VAN CRIEKINGEN, R. BEAUWENS, J. W. JEROME, and E. E. LEWIS, “Mixed-Hybrid Discretization Methods for the Linear Boltzmann Transport Equations,” Comput. Methods Appl. Mech. Eng. (accepted for publication).
   Google Scholar
• C. R. E. DE OLIVEIRA, “An Arbitrary Geometry Finite Element Method for Multigroup Neutron Transport with An-isotropic Scattering,” Prog. Nucl. Energy, 18, 1/2, 227 (1986).
   Google Scholar
• G. PALMIOTTI, E. E. LEWIS, and C. B. CARRICO, “VARIANT: VARIational Anisotropic Nodal Transport for Multidimensional Cartesian and Hexagonal Geometry Calculations,” ANL-95/40, Argonne National Laboratory (1995).
   Google Scholar
• J. J. LAUTARD, D. SCHNEIDER, and A. M. BAUDRON, “Mixed Dual Methods for Neutronic Reactor Core Calculations in the Cronos System,” Proc. Int. Conf. Mathematics and Computation, Reactor Physics and Environmental Analysis of Nuclear Systems, Madrid, Spain, September 27–30, 1999, p. 814 (1999).
   Google Scholar
• B. DAVISON, Neutron Transport Theory, Clarendon Press, Oxford (1957).
   Google Scholar
• J. A. DAVIS, “Variational Vacuum Boundary Conditions for a PN Approximation,” Nucl. Sci. Eng., 25, 189 (1966).
   Web of Science ®Google Scholar
• G. YA. RUMYANTSEV, “Boundary Conditions in the Spherical Harmonic Method,” React. Sci. Technol. (J. Nucl. Energy Parts A/B), 16, 111 (1962).
   Google Scholar
• C. B. CARRICO, E. E. LEWIS, and G. PALMIOTTI, “Matrix Rank in Variational Nodal Approximations,” Trans. Am. Nucl. Soc., 70, 162 (1994).
   Google Scholar
• S. VAN CRIEKINGEN, “Mixed-Hybrid Discretization Methods for the Linear Transport Equation,” PhD Thesis, Northwestern University (2004).
   Google Scholar
• E. E. LEWIS, C. B. CARRICO, and G. PALMIOTTI, “Variational Nodal Formulation for the Spherical Harmonics Equations,” Nucl. Sci. Eng., 122, 194 (1996).
   Web of Science ®Google Scholar
• J. J. DUDERSTADT and L. J. HAMILTON, Nuclear Reactor Analysis, John Wiley & Sons, New York (1976).
   Google Scholar
• P. A. RAVIART and J. M. THOMAS, “Primal Hybrid Finite Element Methods for 2nd Order Elliptic Equations,” Math. Comput., 31, 138, 391 (1977).
   Web of Science ®Google Scholar
• S. VAN CRIEKINGEN and R. BEAUWENS, “Mixed-Hybrid Discretization Methods for the P1 Equations,” Appl. Numer. Anal. (submitted for publication).
   Google Scholar
• W. S. YANG, M. A. SMITH, G. PALMIOTTI, and E. E. LEWIS, “Interface Conditions for Spherical Harmonics Methods,” Nucl. Sci. Eng., 150, 257 (2005).
   Web of Science ®Google Scholar
• Y. Y. AZMY, “Multidimensional Linear-Linear Nodal Transport Methods in Weighted Diamond Difference Form,” Proc. Int. Topl. Mtg. Advances in Reactor Physics, Mathematics and Computation, Paris, France, April 27–30, 1987, p. 1005 (1987).
   Google Scholar
• H. KHALIL, “A Nodal Diffusion Technique for Synthetic Acceleration of Nodal SN Calculations,” Nucl. Sci. Eng., 90, 263 (1985).
   Web of Science ®Google Scholar
• M. A. SMITH, G. PALMIOTTI, E. E. LEWIS, and N. TSOULFANIDIS, “An Integral Form of the Variational Nodal Method,” Nucl. Sci. Eng., 146, 141 (2004).
   Web of Science ®Google Scholar
• A. QUARTERONI and F. SALERI, Scientific Computing with MATLAB, Vol. 2 of Texts in Computational Science and Engineering, Springer-Verlag, New York (2003).
   Google Scholar
• A. MESSIAH, Quantum Mechanics, Dover Publications, New York (1999).
   Google Scholar